I’ve traveled to France and met a FEMALE named Elliette. :-) Indeed she said her name different than "Elliot" but again she was French and her name was Elliette. Even if it is "made up" and "modern" who cares? All names are made up at some point.

There are a few famous women with the name - french author, Eliette Abecassis; the Dior model, Eliette von Krajan; the scientist, Eliette Brunel Deschamps.

Its peak popularity was in the 1930’s, but still wasn’t very high. The low popularity combined with the general ignorance of the American population may account for the insistence the name is entirely made up.

Elliette is an Americanization of the name Eliette. The English language, American dialect in particular, prefer to have the consonant in the syllable that matches the sound,
i.e El-lie-ette